Robust Control Method of Melt Level in the Twin Roll Strip Caster

ABSTRACT

The present invention provides a robust control method for maintaining a melt level at a constant value in a mold in a twin roll strip casting process. In the twin roll strip casting process, whether using a stopper system ( 3 ), which is provided in a tundish ( 2 ) to supply melt into the mold, or using a camera system, which measures the melt level in the mold, the robust control method of the present invention controls the melt level both using an advanced controller, which controls, at an initial stage of the casting process or when a disturbance arises, the target value of the melt level such that the target level corresponds to the performance characteristics of the melt level control system, and using a feedback controller, which maintains the melt level at a constant value under normal casting conditions.

TECHNICAL FIELD

The present invention relates to a method for maintaining a melt level at a constant value in a mold in a twin roll strip casting process.

BACKGROUND ART

FIG. 1 schematically shows a twin roll trip casting process. Steel melt which is in a ladle 1 is supplied into a tundish 2 through a slide gate and, thereafter, is supplied into a mold, which consists of casting rolls 6 and edge dams 7, through a stopper system 3 and an immersion nozzle 4. The level of the steel melt supplied into the mold is measured using a camera 5. The supplied steel melt is cooled by the water-cooled casting rolls 6 and formed into a strip 8 through a roll nip. Subsequently, it is wound around a coiler 11 after passing through pinch rolls and a rolling machine.

As such, a system for supplying steel melt into the mold in the twin roll strip casting process includes a stopper and an immersion nozzle. Furthermore, an image processing method using the camera is used as a system for measuring a melt level. Such precision control of melt level in the mold in the twin roll strip casting process is indispensable to ensure stable casting conditions. If the melt level is changed in a twin roll strip casting process, the contact time of the melt with the water-cooled casting rolls is changed, thus deteriorating the quality of the strip to be produced. Furthermore, even a single failure of the melt level control may damage the expensive casting rolls and other components, therefore reliable melt level control must be ensured.

Many studies have been conducted on a method for controlling a melt level in a mold. As examples of the studies, several methods have been proposed in Korean Patent Application Nos. 10-2000-80776 and 10-1996-57612 and in Japan Patent Application Nos. 2001-69265, 1999-141926, 1996-167075 and 1996-110550.

In previously disclosed papers (Control Engineering Practice, 6 (1998), 191-196), rapid change in discharge coefficients of a stopper and an immersion nozzle and a melt supply time delay are regarded as obstacles to stable melt level control in a mold, and many studies have been conducted on them.

To overcome the above-mentioned obstacles, a method using proportional/integral/differential controllers having different characteristics at initial and middle stages of a casting process was proposed (JP-1999-141926). Furthermore, a method in which the rotating speed of the casting rolls is changed to control the melt level when it is impossible to control the melt level using a stopper and an immersion nozzle has been proposed (US-1998-034239).

However, overshoot arises at an initial stage of a casting process. As well, due to disturbances, overshoot may arise at an intermediate stage of the casting process. Furthermore, excessive overshoot may damage a meniscus shield or the casting rolls and reduce the quality of the product and the casting stability. Major causes of such overshoot are changes to melt supply hardware, error in machining refractories, failure of null adjustment to a stopper height, changes in a melt level in a tundish, and changes in a strip manufacturing speed.

In particular, the discharge coefficient of the stopper, which is explained by the following equation (1), is inconstant during a casting process, thus it is very important to efficiently control a melt level to prepare for when a disturbance is induced by the change in the discharge coefficient. discharge coefficient of the stopper=amount of strip manufactured per hour/maximum amount of melt supplied through the stopper outlet   (1)

However, the controller that has been mainly used for controlling the melt level is a PID (proportional/integral/differential) controller, which is widely used because it has advantages of a simple structure and an easy tuning method, but has a disadvantage in that it has difficulty responding to changes in the surrounding conditions and to sudden incidents. Moreover, there is a problem in that it is difficult to apply this controller to a device that requires high restoration expenses.

Meanwhile, a robust controller can easily respond to changes in surrounding conditions and to sudden incidents. However, because it is in the initial stage of development, various mathematical models and evaluation standards are required. Furthermore, there is no precedent for application to steel making or continuous casting fields.

In a twin roll strip caster, even if melt overflows only once, because components of the caster are damaged, a robust controller which does not allow melt to overflow even once is required.

DISCLOSURE OF THE INVENTION Technical Tasks to be Solved by the Invention

Accordingly, the present invention has been made keeping in mind the above problems occurring in the prior art, and an object of the present invention is to provide a robust controller which solves disadvantages of a PID controller and does not allow even one failure, thus being easily applied to an iron manufacturing process.

Technical Solution

In order to accomplish the above object, the present invention provides a robust control method for a melt level in a twin roll strip casting process both using a stopper system, which is provided in a tundish to supply melt into a mold, and using a camera system, which measures the melt level in the mold. The robust control method comprises: controlling the melt level both using an advanced controller, which controls, at an initial stage of the casting process or when a disturbance arises, a target value of the melt level such that the target level corresponds to a performance characteristic of a melt level control system, and using a feedback controller, which maintains the melt level at a constant value under normal casting conditions.

In the present invention, discharge coefficients of a stopper and an immersion nozzle, used in the twin roll strip casting process, a melt feed time delay and a strip manufacturing speed from a stored casting data are obtained, and, thereafter, variable ranges thereof are determined. Subsequently, the target value of the melt level to be controlled by the melt level control system of a twin roll strip caster within the determined variable ranges is set. A robust controller is designed such that the melt level satisfies specifications required in the twin roll strip casting process, despite an outlet closing/opening event resulting in a rapid change in the discharge coefficients of the stopper and the immersion nozzle, thus realizing the target value of the melt level. Furthermore, the robust controller controls the melt level such that the melt level reaches the target value as rapidly as possible, despite minimized overshoot, at the initial stage of the casting process.

The operation of the robust controller, designed as described above, is as follows.

In the case of the initial stage of the casting process, the operation of the robust controller is executed by the steps of: advancing a stopper rod; starting the advanced controller; applying the advanced controller until the melt level reaches a normal value; applying the feedback controller when the melt level reaches the normal value; and maintaining a normal control condition.

Furthermore, in the case that a disturbance arises, the operation of the robust controller is executed by the steps of: detecting the disturbance; starting the advanced controller; starting the feedback controller when the melt level reaches the normal value; and maintaining a normal control condition.

Advantageous Effects

In the present invention, on the basis of experience obtained from executing twin roll strip casting processes, variable ranges of discharge coefficients of a stopper and an immersion nozzle, a melt supply time delay and a strip manufacturing speed are determined. Thereafter, detailed specifications required in a melt level controlling process are determined within the preset variable ranges of the parameters. As a result, there are the following advantages.

In the twin roll strip casting process of the present invention, a time ranging from 8 seconds to 26 seconds is required until a melt level reaches a target value at the initial stage of the casting process. At this time, overshoot is controlled such that the maximum overshoot is within 1% of the target value.

In a middle stage of the casting process, even if the discharge coefficient of the stopper system is changed from 0.4 to 0.8 or the discharge coefficient of the immersion nozzle is changed from 0.45 to 0.85, the melt level is controlled such that a change thereto is within 3% of the target value.

When a melt supply time delay of a stopper system 3 and an immersion nozzle 4, which are used for supplying melt into the mold, ranges from 0.5 seconds to 0.7 seconds, the time required until the melt level reaches the target value at the initial stage of the casting process ranges from 8 seconds to 26 seconds, and the maximum overshoot is within 1% of the target value.

Even if the discharge coefficient of the stopper system 3 is abruptly changed from 0.4 to 0.8 or the discharge coefficient of the immersion nozzle is abruptly changed from 0.45 to 0.85, so that an outlet, which was slightly closed, is normally opened, the melt level is controlled such that it is within 3% of the target value.

Therefore, if the melt level control satisfies the specifications required in the present invention, stability in the casting process and superior product quality are ensured, and accidents which incur high expenses are prevented.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic view showing a twin roll strip casting process;

FIG. 2 is a flow diagram showing a control system of the present invention;

FIG. 3 is a schematic view showing a robust melt level control method in the twin roll strip casting process according to the present invention;

FIG. 4 is distribution graphs showing discharge coefficients of a stopper and an immersion nozzle used in the twin roll strip casting process according to the present invention;

FIG. 5 is graphs showing response characteristics of an advanced controller which executes robust melt level control at an initial stage of the twin roll strip casting process according to the present invention;

FIG. 6 is a data graph showing results of the robust melt level control tests at the initial stage, at which overshoot arises, in the twin roll strip casting process according to the present invention; and

FIG. 7 is a data graph showing response characteristics of the melt level when disturbance arises in the twin roll strip casting process, according to the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, a design of a robust controller of the present invention will be described in detail with reference to the attached drawings.

FIG. 2 is a flow diagram showing a control system of the present invention.

In a process of FIG. 1, the target value of a melt level is input into an advanced controller, and a feedback controller receives feedback related to the melt level and sends an output signal to a stopper, so that the amount of melt, which is supplied into a mold through a nozzle, is adjusted, thus controlling the melt level in the mold. A portion designated by P denotes an equation model which describes hardware including the stopper, the nozzle and the mold. In view of the robust controller, to develop the system, the model is expressed by ranges of important factors. The advanced controller, which is designated by F, is software which is set such that the melt level reaches the target value at the initial stage of the casting process. K denotes the feedback controller, which sends command signals to the hardware such that the melt level is maintained in a desired value.

FIG. 3 is an enlarged view showing a process of supplying melt into the mold of the twin roll strip caster.

A stopper system 3 includes a stopper motor drive system 12, which drives the stopper upwards and downwards, a stopper lever 13, and a stopper rod 14, which adjusts the cross-sectional area A_(s) of a stopper outlet in the tundish. A flow quantity Q_(s) of melt, which is supplied into the immersion nozzle 4 through the stopper outlet, is related both to the melt lever (17, h_(T)) in the tundish and to the level (18, u) of the stopper, and a flow quantity Q_(i) of melt, which is supplied into the mold through an outlet of the immersion nozzle 4, is related both to the melt level (24, h_(i)) in the immersion nozzle and to the area A_(i) of the outlet of the immersion nozzle through the following equations. Q _(S) =C _(S)·√{square root over (2gh _(T))}·A _(S)(u)   (2) Q _(i) =C _(i)·√{square root over (2gh _(i))}·A _(i)   (3)

Here, C_(s) and C_(i) respectively denote discharge coefficients of the stopper and the immersion nozzle, and g denotes acceleration due to gravity. From twin roll strip casting tests of 500 times, C_(s) and C_(i) were expressed as distributions of FIG. 4. The discharge coefficient is defined as (amount of strip manufactured per hour)/(maximum amount of melt supplied through the outlet of the stopper or nozzle per hour).

Furthermore, the amount V_(i) and the level (24, h_(i)) of melt supplied into the immersion nozzle 4 and the amount V_(m) and the level (21, h_(m)) of melt supplied into the mold are explained by the following equations (4) and (5). $\begin{matrix} {{\frac{\mathbb{d}V_{i}}{\mathbb{d}h_{i}} = {{f_{i}\left( h_{i} \right)} = {2{L_{i}\left( {D_{i} + \frac{h_{i}}{\tan\quad\theta_{o}}} \right)}}}},{h_{i} > 0}} & (4) \\ \begin{matrix} {\frac{\mathbb{d}V_{m}}{\mathbb{d}h_{m}} = {{f_{m}\left( h_{m} \right)} = {{L_{R}\left( {{2R} - {2\sqrt{R^{2} - h_{m}^{2}}} + r_{g}} \right)} -}}} \\ {{2{L_{o}\left( {D_{o} + \frac{h_{m} - H_{o}}{\tan\quad\theta_{o}}} \right)}},{h_{m} > H_{o}}} \end{matrix} & (5) \end{matrix}$

Here, L_(i) and D_(i) denote the inside length and inside diameter 25 of the lower end of the immersion nozzle, L_(o) and D_(o) denote the outside length and outside width 26 of the lower end of the immersion nozzle, L_(R) and R denote the length and radius 22 of each casting roll, r_(g) denotes the gap 20 between the rolls, θ_(o) denotes the angle at which the outline of the immersion nozzle is angled and H_(o) denotes the installation height 27 of the immersion nozzle from a nip between the rolls.

In this system, dynamics in a time range t which governs the melt level 21 in the mold is explained by the following equations (6) and (7). $\begin{matrix} {\frac{\mathbb{d}V_{i}}{\mathbb{d}t} = {{Q_{S}\left( {t - T_{S}} \right)} - {Q_{i}(t)}}} & (6) \\ {\frac{\mathbb{d}V_{m}}{\mathbb{d}t} = {{Q_{i}\left( {t - {Ti}} \right)} - {Q_{o}(t)}}} & (7) \end{matrix}$

Q_(o) denotes the manufacturing speed of a strip formed through the roll nip, and T_(s) and T_(i) respectively denote the time delay required to supply melt from the outlet of the stopper to the immersion nozzle and the time delay required to supply the melt from the immersion nozzle to the mold. It is difficult to detect each time delay, but the sum T_(d) of two time delays is calculated from the difference between the time at which closing of the stopper begins when the casting is interrupted, and the time at which the melt level in the mold decreases. Thus, the sum of time delays can be obtained from the stored casting data. In addition, a variation range of Q_(o) can also be obtained from the stored casting data.

Therefore, a control model for controlling the melt level 21 in the mold using the height 18 of the stopper as an input is explained by the following equation. $\begin{matrix} {\frac{\mathbb{d}V_{i}}{\mathbb{d}t} = {\left. {\frac{\mathbb{d}V_{i}}{\mathbb{d}h_{i}} \cdot \frac{\mathbb{d}h_{i}}{\mathbb{d}t}}\Rightarrow\frac{\mathbb{d}h_{i}}{\mathbb{d}t} \right. = {\frac{\mathbb{d}h_{i}}{\mathbb{d}V_{i}} \cdot \left( {{Q_{S}\left( {t - T_{S}} \right)} - {Q_{i}(t)}} \right)}}} \\ {= {\frac{1}{f_{i}} \cdot \left( {{C_{S}\sqrt{2{gh}_{T}}{A_{S}\left( {u\left( {t - T_{S}} \right)} \right)}} - {C_{i}\sqrt{2{gh}_{i}A_{i}}}} \right)}} \end{matrix}$ $\begin{matrix} {\frac{\mathbb{d}V_{m}}{\mathbb{d}t} = {\left. {\frac{\mathbb{d}V_{m}}{\mathbb{d}h_{m}} \cdot \frac{\mathbb{d}h_{m}}{\mathbb{d}t}}\Rightarrow\frac{\mathbb{d}h_{m}}{\mathbb{d}t} \right. = {\frac{\mathbb{d}h_{m}}{\mathbb{d}V_{m}} \cdot \left( {{Q_{i}\left( {t - T_{i}} \right)} - {Q_{o}(t)}} \right)}}} \\ {= {\frac{1}{f_{m}} \cdot \left( {{C_{i}\sqrt{2{gh}_{i}}A_{i}} - {L_{R} \cdot {r_{g}(t)} \cdot {v_{r}(t)}}} \right)}} \end{matrix}$

When this equation is changed into a linear model and is Laplace transformed, it is expressed as the following equation. The parameters used in the equation have variable ranges described in the following Table. $\begin{matrix} \begin{matrix} {{P_{R}(s)} = \frac{Y(s)}{R(s)}} \\ {= {\frac{\kappa_{S} \cdot \kappa_{m}}{\left( {s + \kappa_{i}} \right)\left( {s + \kappa_{o}} \right)}\frac{{15.29s} + 21.7}{s^{3} + {8.5s^{2}} + {23.78s} + 21.7}{\mathbb{e}}^{- T_{d^{S}}}}} \end{matrix} & (8) \end{matrix}$

Y(s) denotes the Laplacian of the actual measured value h_(m) of melt level in the mold, and R(s) denotes the Laplacian of the command value of the height of the stopper. The first polynomial of the right term of the equation is obtained from the equations described above. The second polynomial is obtained by linearly modeling both the stopper height command value R(s) and the actual measured stopper height value U(s). Here, because the dynamics explaining the stopper height respond faster than the dynamics of the melt level in the mold which is in the first polynomial of the right term, the dynamics explaining the stopper height are determined by known constant parameters in order to exclude uncertainty from the dynamics. TABLE 1 Parameter Mean value Variable range κ_(d)  0.33 (1/sec²) 0.21˜0.44 κ_(i)  0.44 (1/sec) 0.35˜0.52 κ_(o) 0.023 (1/sec) 0.019˜0.026 T_(d)  0.6 (sec) 0.5˜0.7

In this table, the variable ranges of the parameters are values considered when the melt level ranges from 410 mm to 450 mm, the melt level in the tundish ranges from 375 mm to 425 mm, the melt level in the immersion nozzle ranges from 26 mm to 54 mm, the strip manufacturing speed at the roll nip ranges from 0.0047 to 0.0116 (m²/sec), the discharge coefficient of the stopper ranges from 0.41 to 0.85, and the discharge coefficient of the immersion nozzle ranges from 0.42 to 0.92.

The performance standard required in the controller of the above-mentioned control model is explained by the following three frequency-domain performance evaluation standards.

1. Stability Evaluation Standard: $\begin{matrix} {{{\frac{{P({j\omega})}{G({j\omega})}}{1 + {{P({j\omega})}{G({j\omega})}}}} \leq 1.8},{{{for}\quad{all}\quad P} \in P_{R}},{\omega \in \left\lbrack {0.1,20} \right\rbrack}} & (9) \end{matrix}$

2. Disturbance Evaluation Standard: $\begin{matrix} {{{\frac{P({j\omega})}{1\quad + \quad{{P({j\omega})}\quad{{G({j\omega})}\quad}}}}\quad \leq \quad 1.03},{{{for}\quad{all}\quad P} \in P_{R}},{\omega\quad \in \quad\left\lbrack {0.1,\quad 20} \right\rbrack}} & (10) \end{matrix}$

The magnitude of the transfer function between the output Y(s) and the input D(s) shown in FIG. 2 is expressed by the left term of the equation (10).

3. Initial Response Evaluation Standard: $\begin{matrix} \begin{matrix} {{{{T_{L}({j\omega})}} \leq {\frac{{P({j\omega})}{G({j\omega})}}{1 + {{P({j\omega})}{G({j\omega})}}}} \leq {{T_{U}({j\omega})}}},} \\ {{{{for}\quad{all}\quad P} \in P_{R}},{\omega \geq 0}} \end{matrix} & (11) \end{matrix}$

The magnitude of the transfer function between the output Y(s) and the input R(s) shown in FIG. 2 is expressed by the left term of the equation (10). Frequency domain and time domain response characteristics of T_(L) and T_(U) are shown in FIG. 5. $\begin{matrix} {T_{L}\left( {{{\left. {jw} \right) = \frac{0.0225}{\left( {s + 1} \right)\left( {{10s} + 1} \right)\left( {s^{2} + {0.2036s} + 1} \right)}},}} \right.} & (12) \\ {{T_{U}\left( {j\quad w} \right)} = \frac{\left( {\frac{s}{0.18} + 1} \right)}{\left( {\frac{s}{0.4} + 1} \right)\left( {\frac{s}{0.3} + 1} \right)\left( {\frac{s}{0.2} + 1} \right)}} & (13) \end{matrix}$

The robust controller which satisfies the above-mentioned evaluation standards comprises the following advanced controller and feedback controller.

Advanced Controller: $\begin{matrix} {{F(s)} = {\frac{1}{\left( {\frac{s}{0.5} + 1} \right)}\frac{0.48}{s^{2} + {1.224s} + 0.1296}}} & (14) \end{matrix}$

Feedback Controller: $\begin{matrix} {{G(s)} = \frac{0.016\left( {\frac{s}{0.02} + 1} \right)\left( {\frac{s}{0.4} + 1} \right)}{{s\left( {\frac{s}{2} + 1} \right)}\left( {\frac{s}{9} + 1} \right)\left( {\frac{s}{100} + 1} \right)}} & (15) \end{matrix}$

As described above, the present invention serves to maintain a constant melt level in a twin roll strip casting process. Performance standards of a robust controller are set such that they are insensitive to inconstant discharge coefficients of a stopper and an immersion nozzle, and to a variable strip manufacturing speed and melt supply time delay, which act as obstacles to maintenance of a constant melt level, thus the height of the stopper is controlled by the robust controller.

In the present invention, analog signal processing advanced controller and feedback controller, which serve to maintain the constant melt level in the twin roll strip casting process, may be replaced with digital signal processing controllers, so that they are applicable to a computer system which includes a real-time operating system that precisely realizes time synchronous of an application program of a user.

Thus, as shown in FIG. 6, showing results of the robust melt level control tests in the twin roll strip casting process, it is confirmed that the melt level in the mold is controlled at an initial stage of a casting process such that it takes 8 to 26 seconds to increase the melt level to the target value, and an overshoot is within 1% of the target value.

Furthermore, as shown in FIG. 7, showing results of the robust melt level control tests in the twin roll strip casting process, it is confirmed that, when a disturbance arises, an overshoot is within 3% of the target value and the melt level is returned into the normal value in a short time. 

1. A robust control method for a melt level in a twin roll strip casting process both using a stopper system, which is provided in a tundish to supply melt into a mold, and using a camera system, which measures the melt level in the mold, the method comprising: controlling the melt level both using an advanced controller, which controls, at an initial stage of the casting process or when a disturbance arises, a target value of the melt level such that the target level corresponds to a performance characteristic of a melt level control system, and using a feedback controller, which maintains the melt level at a constant value under normal casting conditions.
 2. The robust control method of the melt level in the twin roll strip casting process according to claim 1, wherein a process of designing both the advanced controller and the feedback controller comprises the steps of: obtaining discharge coefficients of a stopper and an immersion nozzle, used in the twin roll strip casting process, a melt feed time delay and a strip manufacturing speed from a stored casting data and determining variable ranges thereof; setting the target value of the melt level to be controlled by the melt level control system of a twin roll strip caster within the determined variable ranges; and designing a robust controller such that the melt level satisfies specifications required in the twin roll strip casting process, despite an outlet closing/opening event resulting in a rapid change in the discharge coefficients of the stopper and the immersion nozzle, thus realizing the target value of the melt level.
 3. The robust control method of the melt level in the twin roll strip casting process according to claim 1, wherein application of the advanced controller and the feedback controller comprises the steps of: starting the advanced controller at the initial stage of the casting process or when a disturbance arises; applying the advanced controller until the melt level reaches a normal value; and applying the feedback controller when the melt level reaches the normal value.
 4. The robust control method of the melt level in the twin roll strip casting process according to claim 1, wherein the advanced controller is set such that a time ranging from 8 seconds to 26 seconds is required until the melt level reaches the target value at the initial stage of the casting process, and such that a maximum overshoot occurring at the initial stage is within 1% of the target value.
 5. The robust control method of the melt level in the twin roll strip casting process according to claim 1, wherein the feedback controller is set such that, when the discharge coefficient of the stopper system is abruptly changed from 0.4 to 0.8 or the discharge coefficient of the immersion nozzle is abruptly changed from 0.45 to 0.85 so that the outlet, which has been slightly closed, becomes normally open, the melt level is within 3% of the target value.
 6. The robust control method of the melt level in the twin roll strip casting process according to claim 1, wherein the feedback controller is set such that, even if a time required to feed the melt into the mold through both the stopper system and the immersion nozzle is delayed for 0.5 seconds to 0.7 seconds, the maximum overshoot at the initial stage of the casting process is within 1% of the target value, and such that, even if the discharge coefficient of the stopper or the immersion nozzle is abruptly changed from 0.4 to 0.8 or from 0.45 to 0.85, the melt level is within 3% of the target value. 